Meniscus Dynamics in Aluminium Extrusion Ingot Casting

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Preface

This work was funded by the Research Council of Norway (NFR), Hydro Alu- minium ASA and Elkem Aluminium ANS, through the PROSMAT research project. The last four months were funded by the department of Materials Technology and Electorchemistry at the Norwegian Institute of Science and Technology (NTNU).

My supervisors were professor Jon Arne Bakken at the department of Materials Technology and Electrochemistry, NTNU and professor II Stein Tore Johansen at the department of Applied Mechanics, Thermo- and Fluid Dynamics, NTNU.

Casting tests were performed at Hydro Aluminium Sunndalsøra under the supervision of Steinar Benum and Jon Erik Hafsaas of Hydro Aluminium.

Dag Mortensen of the Institute for Energy Technology (IFE) provided material parameters for the casting simulations.

Parts of the work have earlier been presented at TMS conferences, with a paper published in the proceedings of the Computational Modelling con- ference in 2001:

A Marker Chain Front Tracking Method Adapted for Modelling Menis- cus Dynamics in the Direct Chill Al Billet Casting Process ,Cast Shop Technology, 2001 TMS Annual Meeting.

A marker chain front tracking method for modelling meniscus dynamics in the Al ingot casting process, Computational Modelling of Materials, Minerals and Metals Processing, TMS 2001.

Sadly, I will not be continuing the work of developing the casting process.

But hopefully the results, both the development of the numerical free surface methods and the conclusions drawn regarding the casting process, will come to further use. There is a lot of work remaining to be done in both fields, and I do believe that significant improvement to the casting process through better meniscus control is possible.

I especially want to thank professor Jon Arne Bakken for always having time for a discussion, and for his patience with my enthusiasm. I also want to thank professor II Stein Tore Johansen for his valuable help and advice with model implementation in the FLUENT code.

Finally I want to thank my fianc´e Gerd, and especially my eleven month old son Brage Ois´ın, for reminding me that there are more important things than a Dr.Ing. thesis.

Trondheim, 15. April 2002

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Summary

In the modern process of continuous Direct Chill (DC) hot top casting of aluminium extrusion ingot with gas slip [25], poor surface quality of the cast ingot can still be a problem. In the worst cases pronouncedsurface wrinkling may occur coupled with periodic zones ofreduced grain size,macrosegregation andexudationat the surface. The observed surface irregularities are believed to be linked to periodic surface oscillations or folding of the meniscus resulting in varying solidification conditions in the mould.

The focus of this work is to gain a better understanding of the dynamics of the free aluminium surface, ormeniscus, formed in the mould, and the effect it has on ingot surface formation. Both casting experiments and numerical simulations of the casting process have been performed. In addition a brief analytical analysis of oscillations and waves that may influence the meniscus behaviour has been made, and finally a series of simple meniscus water model experiments have been performed.

The main part of the work consists of the adaption and implementation of a two-phase marker chain front tracking technique using cubic spline surface reconstruction, the Method of Tensions (MOT) [49]. This method is applied in modelling the free surface meniscus dynamics. The advantage of this type of model is its accuracy in the calculation of surface tension forces, which is especially important in the case of modelling the Al meniscus due to the high metal gas density ratio. Also, with this model wetting conditions may easily be implemented as boundary conditions on the surface spline function.

Modifications have been made to marker advection, surface reconstruction, and surface force distribution algorithms of MOT to improve surface stability and phase conservation.

In the solidification modelling the effect of latent heat release is included in the heat capacity so that a direct temperature-enthalpy relation is pre- served. Further a simple model for the solidification contraction is implemented to correctly model both the heat flow across and the slip gas flow through the air gap.

The modified MOT is implemented together with the solidification model

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in the FLUENT CFD solver, which uses the SIMPLE algorithm [47] together with the Power Law [1] in the Finite Volume discretization.

The work has lead to two important contributions:

Firstly, a functional numerical method for modelling meniscus dynamics in the casting process has been developed.

Secondly, added insight into the casting process has been achieved, primarily though the casting tests and casting simulations.

The most important result, indicated by both casting tests and simulations, is that the meniscus oscillations are coupled with significant upward bubbling through the melt inlet in the mould. This conclusion is based on both visual observations of bubbling at the melt surface in the mould and from simulated upward bubbling from the meniscus. Also, the high stability of the section of the meniscus closest to the mould wall, observed in the casting experiments and recreated in casting simulations, imply a large meniscus with at least periodic contact with the melt inlet corner. The results also indicate that a significant upward gas discharge is necessary to induce the rapid meniscus collapse observed in the casting tests. It is believed that the momentum of the fluid flow induced by upward bubbling induces the collapse.

Based on the results achieved, some suggestions are made for process modifications. Firstly, to achieve as smooth a behaviour as possible, the geometry of the inside of the hot top should be smooth. And improved control of the meniscus may be achieved with a modified mould geometry so that meniscus oscillations are reduced. Possible modifications are suggested.

To further develop mould geometry and slip gas control, casting tests should be performed with the modified mould geometry. Also, numerical simulations should be performed with surface breakup and merging techniques implemented in the simulation program, so that bubble formation and coalescence may be included. Subsequently, the upward discharge of slip gas, which is believed to be linked to meniscus collapse, may be properly simulated.

To conclude, the modified Method of Tensions is shown to be accurate and stable enough to be applied to modelling of the meniscus dynamics.

And for the casting process, by altering mould geometry and improving slip gas control, it should be possible to achieve a more stable meniscus, and subsequently a more stable casting process, which should result in improved cast ingot surface quality.

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Chapter 1 Al ingot casting

1.0.1 A brief history of aluminium ingot casting

The history of Al ingot casting stretches back to approximately 100 years ago.

At this time the process of casting steel and copper ingots was already well developed. The ingots were solidified in permanent moulds (book-moulds) into which the molten metal was poured. Initially this technique was also used for production of aluminium ingot, but because of the dangers of the reactivity of the molten aluminium with the atmosphere modifications had to be made. A technique of tilting the mould [9] was developed (see figure 1.1).

By using this technique a gentler melt flow was achieved making for a safer casting process.

Increasing industrialization in the early 20th century, and especially the rapidly growing aviation industry, resulted in a need for increased ingot size.

Larger ingots allowed for production of larger parts so larger planes could be made. These larger ingot dimensions, however, led to new problems in the casting process. The considerable air gap produced by shrinkage of the casting lead to poor heat transfer, slow solidification, and resulted in extremely coarse grain structures. Large intermetallic particles in the coarse structure could cause fracture during rolling and forging, or if cracks were avoided in this process then fractures could appear later in the finished product.

The consequence of the problems connected to large ingot size was the development of the Direct Chill (DC) ingot casting process [16]. The basic idea of DC casting is cooling the ingot by a jet of running water as the ingot emerges from an open mould. Through this open casting technique many of the problems connected to the slow solidification were avoided and the ingot quality was greatly improved.

As requirements for ingot quality further increased new casting techniques were sought to better control the properties of the castings. An important

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2 CHAPTER 1. AL INGOT CASTING

Figure 1.1: Permanent mould casting; tilting-mould technique.

factor in ingot quality was found to be the height of the metal head in the mould. A lower metal surface lead to a shortening of the air gap between the mould wall and ingot surface and subsequently reduced heat extraction through the mould wall. Thereby the properties of the ingot were made less dependent on the primary cooling (see below), which is difficult to control, and thus improving ingot quality [44]. One of the best ways to achieve a lower metal surface in the mould was found to be by the use of a header box of insulating material, a ’hot top’, on the top of a short mould [7]. The method was further developed in the late 1960’s and early 1970’s resulting in a similar geometry to the one used in hot top moulds today. With such good control of metal height, ingot quality could be further improved. Also simultaneous casting of multiple ingots in a multistrand unit was made possible.

Another problem which needed to be dealt with was the poor surface quality of the ingots cast with the hot top DC casting process. For ingots used for rolling poor surface quality is not a problem, since ingots are normally scalped before the rolling process [5]. But for extrusion ingots, which are generally not scalped, better surface quality would greatly influence the finished product. Further developments towards solving the problem of poor surface quality were suggested by Showa in the late 1970’s. By injecting gas into the top of the mould a better control of the shape and position of the free

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1.1. PROCESS DESCRIPTION 3

Figure 1.2: Casting table seen from above. 24 moulds.

melt surface in the mould (also known as the meniscus) could be achieved.

With this technique it was possible to further reduce the air gap and consequently reduce the heat transfer over the gap, thereby further improving the ingot quality. The technique is known as gas slip or air slip casting.

Several different casting techniques have been developed in parallel with the development of the process described above. The three other techniques used today [5] are conventional open DC moulds, air/gas slip moulds with the original Showa-Denko design, and electromagnetic moulds.

The casting method considered in this work is the hot top DC air/gas slip method. A better understanding of the meniscus dynamics and solidification in the mould is sought mainly through mathematical modelling and subsequent numerical simulation. The motivation for this work is to further improve the cast ingot surface quality. The process is described more thor- oughly in the following section. Through this description the current general understanding of the casting process is presented. And some new models are suggested.

1.1 Process description

The contemporary continuous Al hot top DC gas slip extrusion ingot casting process is schematically described in figures 1.2 to 1.4(b). The molten metal flows from the holding furnace onto the casting table (figure 1.2) where it is distributed through channels into a matrix of open moulds. A typical casting

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Figure 1.3: Hot top casting of extrusion ingots.

mould is presented in figure 1.4(a). The melt flows into the mould where it is initially supported by the mould wall and a bottom block. As the metal solidifies the bottom block is withdrawn and as the solid ingot emerges it is further cooled by a water spray which hits the ingot directly below the mould wall (figure 1.4(b)). This is referred to as Direct Chill. A picture of an actual casting process is shown in figure 1.3.

1.2 Solidification

The characteristics of the solidification depend on a multitude of variables such as alloy content, cooling efficiency, mould geometry, melt flow and casting velocity. The influences and effects of these most important factors are considered below.

1.2.1 Hot top

As described above the hot top controls the level of the melt in the mould, thereby improving ingot quality and also stabilizing the casting process. The hot top is made of an insulating material so that the heat extraction from the ingot through the hot top will be minimal.

1.2.2 Mould geometry

Several different types of mould geometry are used in the casting process.

The geometry presented here (figure 1.4(a)) is chosen partly to facilitate gridding of the computational domain in the numerical simulations. One important aspect of the geometry is the extra space for the gas pocket above the meniscus. Through developments of the casting process one has found

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1.2. SOLIDIFICATION 5

(a) Cross section of casting with enlarged mould wall and definition of meniscus region. Melt flow direction indicated in melt inlet.

(b) Cross section of meniscus region. Closed air gap, free meniscus.

Figure 1.4: Ingot casting with meniscus.

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6 CHAPTER 1. AL INGOT CASTING that extra space above the meniscus stabilizes the primary solidification. A partly sloping bottom surface of the hot top is often used.

1.2.3 Lubrication and gas injection

Lubrication systems were developed in parallel with the development of DC casting [42]. During casting lubricating oil is injected into the top of the mould to lubricate the mould wall, thereby allowing the ingot to slip. New methods have gradually been developed for the injection of both gas and oil into the mould. In the specific process considered here the air and oil are introduced into the mould through a porous graphite ring (figure 1.4(a)) in the mould wall. The gas is injected through the upper part of the ring while the air is injected through the lower part. This technique is used in both the Wagstaff AirSlip [33] and Hydro Air Cushion techniques, among others.

1.2.4 Cooling

There are two main sources of cooling: the mould wall and the direct water chill.

The mould wall is composed of two separate regions: a porous graphite ring and an aluminium casing encapsulating it (figure 1.4(a)). Both these regions are cooled by a water reservoir inside the mould. As the metal comes into thermal contact with the mould wall it is cooled and a solid shell may form, known as thesolid lip. This cooling by the mould wall is known as the primary cooling.

The second and main source of cooling is the Direct Chill. As the ingot emerges below the mould it is sprayed with water (figure 1.4(b)). The water cools the ingot as it runs down along its surface. This region of water cooling is known as the ’secondary cooling’ zone. The water chill efficiency determines the properties of the bulk of the cast ingot while the primary cooling mainly effects the ingot surface properties.

1.2.5 Mushy zone

Alloy elements induce a broadening of the solidification temperature range.

Pure aluminium goes from complete liquid to complete solid at a specific temperature, whereas aluminium alloys, due to segregation, solidify over a finite temperature range. The temperature range of solidification increases with the amount of alloy elements added. This is the reason for the so called

’mushy zone’ between the liquid and solid (see figure 1.4(a)). At the top of the region where the temperature is at its highest, fine ’equiaxed’ grains with

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1.2. SOLIDIFICATION 7 no preferred growth direction are formed which float freely in the melt. The extent of grain formation in the melt depends on the particular aluminium alloy considered. At the lower part of the mushy region dendrites grow from the solid region extending out into the mushy. Dendrites will also form in the primary cooling zone growing inward from the mould wall. As the grains formed in the mushy zone grow and settle around the dendrites growing at the bottom of the zone the metal grows in strength and eventually becomes rigid.

The temperature at which the solidified metal forms a connected structure is known as the point of dendrite coherency. Solidification contraction (see 1.2.7) will start at some temperature below this point, depending on the properties of the specific aluminium alloy.

1.2.6 Heat transfer

Primary cooling

The heat transfer from the melt to the hot top is negligible compared to the primary and secondary cooling described above. So normally the ingot will start solidifying only after making thermal contact with the mould wall (figure 1.4(b)), resulting in the solid lip described above. The heat transfer from the ingot to the mould in the primary cooling zone will depend on the amount of physical contact between the ingot and the mould, the width and length of the air gap, the composition of gas and oil in the air gap and the emissivity of the mould and ingot surfaces. If the ingot is in physical contact with the mould then the heat transfer in the region of contact will dominate the other heat transfer from ingot to mould. In this case the air gap is closed (as in figure 1.4(b)). When there is no contact between mould wall and ingot the air gap is open. In this case slip gas passes through the gap and exits below the mould. Gas flow is discussed in section 1.3.4. The heat conduction across the air gap is determined by the gap width and the composition of the oil/gas mixture in the gap. Increased oil content will result in increased conduction. The emissivity of the mould and ingot surfaces will influence the radiative heat transfer across the gap. Another factor which might influence the heat transfer over the air gap could be surface oxide passing through it.

Formation of aluminium oxide (alumina) is discussed below (1.3).

Secondary cooling

With given alloy properties, the direct water chill , being the main cooling source, determines the solidification rate and extent of the mushy zone in the bulk of the ingot. The water impingement area can be seen in figure 1.4(b). In

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8 CHAPTER 1. AL INGOT CASTING addition, the secondary cooling can to a lesser extent effect the temperature field, and consequently the solidification, in the primary cooling zone.

The effect of the secondary cooling depends on the mechanism of heat transfer between the ingot and the cooling water and on the temperature difference between the ingot surface and bulk water temperatures. Film boiling will often occur in the upper area of contact between water and ingot. This type of boiling produces an insulating layer of water vapour on the surface of the ingot, thereby reducing the cooling effect of the water.

The transitions from nucleate boiling to unstable film or transitional boiling, and further to film boiling, [43] are dependent on water properties (see [29]).

Therefore the quality of the water can greatly influence the efficiency of the secondary cooling.

1.2.7 Contraction

As pure aluminium solidifies it will contract to a considerable extent because of the reordering of atoms into the metallic crystal lattice structure.

Excessive contraction can cause serious problems in castings, such as large cracks in the center (hot tearing) or bottom of the ingot (see [19]). There- fore alloy elements are normally added. Through the formation of eutec- tic/peritectic/hypoeutectic the crystal lattice is split up into sections ([19]).

Some alloy elements form compounds which contract less than the aluminium. Consequently the total contraction is reduced. The alloy content will to a great extent determine the total radial contraction of the ingot.

The radial contraction in the mould is determined by the balance between the force of solidification contraction in the solid lip, the force of the total metallostatic head in the mould and possibly also the pressure in the gas pocket , which determines the pressure drop through the open air gap. The mean pressure of the metallostatic head is determined by the mean metal level at the top of the mould. The instantaneous metal height will however vary due to both waves on the casting table and to variations in gas pocket volume.

This leads to variations in air gap width. The radial contraction in the mould also depends on the thickness of the solid lip, which is determined by the intensity of the primary and secondary cooling. Since the amount of primary cooling is partly determined by the radial contraction in the mould this system constitutes a feedback loop, which may lead to a physically unstable air gap. The thickness of the solid in the vertical cross section directly below the primary cooling zone, which is mainly determined by secondary cooling, will also influence the radial contraction, and hence the air gap, in the mould, since the solid lip is supported by the solid metal below. Consequently the strength and radial contraction in the in the secondary cooling zone will

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1.2. SOLIDIFICATION 9

Figure 1.5: Intersection of cast ingot surface showing irregularities.

influence the contraction in the mould.

1.2.8 Segregation

Several kinds of macrosegregation can occur in the surface region of the cast ingot. The four main types (again from [5]) areperiodic segregation, segregation linked toexudation,depleted bands, and acontinuous surface segregation layer. The characteristic periodic segregation occurs in alloys with a short solidification temperature range. The effect is probably linked to periodic

Figure 1.6: Typical oscillations marks on surface of cast ingot.

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10 CHAPTER 1. AL INGOT CASTING remelting of the solid lip, described in [16]. The second type, exudation, is linked to alloys with a broad solidification range. This effect might also be linked to remelting, but here with resulting bleeding or exudation through the semi-solid surface. Another possible cause is folding of the meniscus, also leading to exudation. The third type of segregation, banding, is probably also linked to meniscus behaviour. The second and third type of exudation are discussed further below in section 1.3 . The fourth type, the continuous segregation layer, is a naturally occurring enriched layer appearing in ingots of all alloy types, created by diffusion of alloy elements and melt flow during solidification. Also see [65].

1.2.9 Grain structure

The grain structure might or might not be linked to segregation. The banded segregation described above often occurs coupled with a finer grain structure.

A possible explanation for this phenomenon is solidification of the meniscus, again discussed below (1.3).

1.2.10 Solidified surface

There are at least three typical physical irregularities that occur on the cast ingot surface. These areoscillation marks (also known assurface marks [2]), bleed bands, and thegrain refined segregated bands. These faults are presented schematically in figure 1.5. The oscillation marks are regular periodic grooves in the ingot surface. The bleed bands, caused by exudation (or bleeding) mentioned above, form segregated bulges on the ingot surface, and will often cover the oscillation marks (see [5]). Both the oscillation marks and the bleed bands have the same period as the bands of finer grain structure, suggesting that these periodic defects are all formed by the same mechanism, which is discussed further below (1.3). Also see [62] and [2]. A typical cast ingot surface with oscillation marks is shown in figure 1.6.

1.3 Meniscus dynamics

The meniscus geometry and dynamic properties will greatly influence the solidification in the primary cooling zone. The mean geometry of the meniscus is mainly determined by the mould geometry (particularly the level of the hot top), the slip gas flow rate, and the casting velocity. The geometry influences the metal level at the mould wall and consequently also the length of the air gap. It also influences the periods of open and closed air gap.

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1.3. MENISCUS DYNAMICS 11

Figure 1.7: Pressure difference related to curvature at top of meniscus. Gas pressurepg, metallostatic head pressure pm.

By the discussion above (section 1.2), the air gap influences the amount of primary cooling, and consequently also the ingot surface quality. Therefore controlling the meniscus is of primary importance in the casting process.

Many factors influence the meniscus properties and dynamics. These include wetting boundary conditions at the mould wall and hot top, surface tension coefficient and oxidation on the meniscus. Both the solid lip and the extent of the mushy zone below the meniscus will influence its movement. Subsequently meniscus dynamics and ingot solidification is a two-way interaction. If there is solidification up onto the meniscus the movement is constrained, otherwise the meniscus is here defined as a free meniscus (see figure 1.4(b)).

1.3.1 Surface tension and Wetting

The curvature of the free molten metal surface is determined by the surface tension forces and the pressure difference over the surface (by Laplace’s for- mula [40]). An increase in surface tension coefficient will give a decreased surface curvature with other parameters equal. A fixed wetting angle between the molten metal surface and the mould puts an extra constraint on the meniscus shape. However, in order for the pressure difference between the gas pocket and the metal pressure at the bottom of the hot top to vary freely, the curvature at the contact point between the molten meniscus free surface and the hot top must be free to balance the arbitrary pressure difference (see figure 1.7). To avoid an extra constraint on curvature the wetting angle at this point must also be free.

Tests have shown that the static wetting angle between liquid aluminium

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Figure 1.8: Extreme upper meniscus contact points.

and ceramics (as in the ceramic hot top) is quite small (see [22]). However, in a dynamic system the wetting behaviour may differ from that of the static case.

Also it might be possible that the meniscus could be hanging on a corner of the hot top, thereby allowing it to have free wetting. There are two possible corners to hang from on the hot top bottom: next to the melt inflow and next to the gas pocket. Meniscus dynamics should differ considerably for these two cases (see figure 1.8). Wetting conditions are made subject to analysis in the following modelling work to gain a better understanding of the process.

1.3.2 Oxidation

Aluminium oxide or alumina, Al₂O₃, forms on molten aluminium in contact with an oxygen-rich atmosphere. In the hot top gas slip casting process the molten aluminium is in contact with air on the casting table. As the aluminium flows into the mould the oxide formed can be pulled down and thereby effect the surface formation of the cast ingot. If there is oxygen in the slip gas then oxide will also form on the meniscus surface. Both the oxide pulled into the mould and the oxide formed on the meniscus will influence the dynamic properties of the meniscus. Resolving the free meniscus dynamics will in this case be a three phase problem, with gas, oxide, and molten metal phases present, and the applied free surface approximation (see chapter 4) might not any longer be valid. The following discussion is however based on free meniscus surface movement (unless it is constrained by solidification).

Effects of oxidation will be considered in the later discussion. For now it can

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Figure 1.9: Gravity induced oscillations in casting column.

be stated that a lot of oxidation can make the meniscus more rigid and may also lead to highly irregular meniscus behaviour.

1.3.3 Meniscus oscillations

Several observations have been made of meniscus dynamics in the mould ( [2], [68], [67], [14]). Based on these results and results of observations made during this work (see 2), some models for meniscus dynamics and interaction with solidification are suggested in the following.

Waves on meniscus surface

Oscillations of the meniscus can take several forms. The dynamic properties of the free surface are partly influenced by gravity, surface tension forces (or capillary forces), and wetting. One form of oscillation that might occur is capillary waves, i.e. waves provoked by surface instability where the dominating restoring force is the surface tension force. Or if the restoring forces are the combined surface tension and gravity forces then gravity-capillary waves occur. Gravity waves in the casting column might also occur. In this case the upper surface of the molten metal in the mould oscillates in combination with the meniscus surface (see figure 1.9). The reason for this type of oscillation can be surface waves propagating on the molten metal surface on the casting table, or the oscillation might be induced by gas escaping intermittently from the gas pocket. The amplitude and sustainability of these gravitational oscillations will depend on the damping in the gas pocket, which is dependent on the compressibility of the gas and the flow of gas through the open air gap or bubbling through the mould inlet. An analysis of the influence of the different types of waves is analyzed in chapter 3.

Solidification of the meniscus can also be linked to oscillations.

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Figure 1.10: Collapsing meniscus model.

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Figure 1.11: Surface mark formation model of Ackermann et al.

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16 CHAPTER 1. AL INGOT CASTING Solidification and collapse of the meniscus

Molten meniscus If there is no meniscus solidification the molten meniscus must be supported by the mould wall. However, the slip gas injected must have some form of escape. And if there is no downward escape route it must bubble up through the melt inlet. So with a molten meniscus intermittent upward gas discharge is to be expected.

Meniscus solidification

With sufficient primary cooling, solidification of the lower part of the meniscus can occur, as shown in figure 1.10(a). In this case meniscus oscillations might be connected to formation of surface irregularities. The extent of the solidification will determine the amplitude of the meniscus oscillations and resulting surface faults. The complete process is illustrated in figure 1.10.

Four stages of an oscillation period are shown. The casting direction is towards the left (compare to figure 1.4(b)). The initial state is shown in 1.10(a), where the lower part of the meniscus is solid. When there is solidification on the meniscus a geometry as in figure 1.4(b) is mechanically unstable because the surface forces are not balanced according to Young’s equation [58]. To achieve mechanical equilibrium a partial overflow of the melt over the solidified lower part of the meniscus is necessary. (A similar case which can easily be observed is the meniscus formed when a glass is overfilled with water). The wetting angle at the lower point of the liquid meniscus is then determined by Young’s equation. The meniscus surface shape for a given gas pocket volume is consequently determined by the boundary conditions and the balance of forces through the extent of solidification, the wetting angle at the lower point of the liquid meniscus, the surface tension coefficient, the profile of the pressure jump across the surface and the gravitational forces pulling on the molten metal.

As the ingot is pulled down during casting the solid lip follows, thereby lengthening and deforming the meniscus. Now two things may happen: the meniscus may collapse, or the meniscus may solidify because of thermal contact with the mould wall.

Collapsing meniscus model If the forces over the meniscus can no longer be balanced at some point due to dominating gravitational forces, it will collapse as shown in 1.10(b) - 1.10(c). Subsequently a new meniscus is formed above the old solidified lower part of the meniscus, and the new meniscus surface in contact with the wall solidifies and forms a new solid shell, as shown in 1.10(d). This brings us back to the initial state in 1.10(a).

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1.3. MENISCUS DYNAMICS 17 Solidification or surface tension forces or both may hinder the new meniscus from completely filling the gap between the old meniscus and the mould wall. Curvature and consequently surface tension forces at the lower point of the liquid surface will increase as it collapses toward the wall. The increased curvature and the resulting surface tension forces could prevent complete regaining of wall contact at the lower point of the old meniscus. And also solidification of the collapsing meniscus, stopping its downward movement, might prevent complete filling of the gap. The result will then be a small groove or oscillation mark in the cast ingot surface as shown in figure 1.5.

Internal structural bands might be coupled with the oscillation marks.

The upper part of the solidified meniscus solidifies quickly, leading to a fine grain structure . The metal that runs over the old meniscus when the meniscus collapses solidifies more slowly. After the collapse of the meniscus the regions above and below the thin surface shell of the old meniscus solidify due to increased heat transfer from contact with the mould wall. Consequently a coarser grain structure is formed in these regions. Different alloy content due to different segregation on the solidified surface and inside the ingot may also influence the grain structure. In this way the irregular grain structure described in 1.2.9 might occur, possibly coupled with varying segregation.

Semi steady state A combination of the collapsing meniscus and the molten meniscus models might also occur. After the collapse of the meniscus the formation of the solid shell might not be instantaneous. In the phase before the solid shell grows sufficiently strong to pull the meniscus down, the meniscus dynamics could be as described for the molten meniscus above.

Once the solid shell has gained enough strength to pull the meniscus down the collapsing meniscus phase is again initiated. And so on. Oscillation marks and structural bands (figure 1.5) would probably not be as distinct by this process, but more bleed bands might form, due to a longer period before solidification.

Surface mark formation model of Ackermann et al The second mechanism for oscillation mark formation, which gives similar results to the collapsing meniscus model described above, is the ’Surface mark formation model’ presented in [2]. In this case the free lower contact point of the meniscus, driven by the gravitational pull on the melt, moves down the old solid meniscus surface until it touches the mould wall and solidifies. The cycle is illustrated in figures 1.11(a) to 1.11(d). In this case more remelting of the old meniscus would be expected than for the case of the collapsing meniscus.

So the internal structural bands might be less distinct. The oscillation marks

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18 CHAPTER 1. AL INGOT CASTING should however be of approximately the same size as for the case of meniscus collapse.

It is very possible that the process of oscillation mark formation can be a combination of the ’collapsing meniscus’ and ’surface mark formation’

models.

Exudation In the case of meniscus solidification oscillations there is a much greater chance of exudation leading to the bleed bands (figure 1.5).

After the new meniscus has collapsed or started resolidification the new ingot surface will not be solid. If there is a groove or oscillation mark below the partly solidified new surface the metal head may force melt out through pores in the metal surface into the groove, causing exudation, possibly thereby covering the oscillation marks. If there is an open air gap between the old meniscus and the wall the exuded liquid metal may partly flow down into the gap. This effect may create the characteristic bleed bands shown in figure 1.5. It would both explain the periodicity of the bands and the fact that they are in phase with the internal structural bands. A similar explanation is suggested in [5].

1.3.4 Slip gas flow

Gas discharge from the gas pocket is determined by the meniscus dynamics and solidification. A common technique during casting startup is increasing injected gas flow until the gas starts bubbling up through the melt inlet and then decreasing the gas flow until bubbling is no longer visible. As already described, the meniscus reduces the ingot to mould contact in the primary cooling zone, thereby improving casting control. Making the gas pocket volume as large as possible results in a large meniscus and small ingot/mould contact area. This effect is sought through the startup procedure. In the proceeding casting process it is important to maintain a large gas pocket.

Therefore knowledge and control of gas flow in and out of the gas pocket is important for controlling the cast ingot surface quality.

The injected gas has two possible ways of exiting the gas pocket. The gas can either flow down through the air gap, if it is open, or the gas can escape upwards bubbling through the melt inlet at the top of the mould.

Downward discharge

If the lower part of the meniscus is solidified then the air gap will open a clear passage between the mould wall and the ingot through which the gas escapes from the gas pocket. If the meniscus is completely molten, then there

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1.3. MENISCUS DYNAMICS 19 is no free passage and the air from the gas pocket can not escape downwards.

But if the meniscus dynamics are like those described in either the collapsing meniscus model or the surface mark formation model, then gas flow from the pocket through the air gap should be possible, at least intermittently.

As figure 1.10 illustrates, for the collapsing meniscus model, the passage down along the mould wall is only blocked for a short period after the meniscus collapse. At all other stages the air gap is open. In the case of the surface mark formation model, either the passage is open continuously or there is periodic blocking due to contact between the new meniscus and the mould wall before the meniscus solidifies. So both mechanisms include either intermittent or continuous downward gas discharge.

Upward discharge

If the gas pocket fills to such an extent that the upper contact point of the meniscus passes the lower corner of the melt inlet then the gas will bubble upward through the melt inlet.

Slip gas balance

The injected gas flow rate will determine what fraction of gas flows up and what fraction flows down for each particular solidification mechanism described above. If the injected and downward gas flow rates are not balanced then two things may happen. If the mean injected flow rate is larger than the mean downward flow rate the gas pocket will grow until there is upward gas discharge and the process will repeat itself. If the mean injected gas flow rate is smaller than the mean downward flow rate then the gas pocket will empty, and the casting might freeze to the mould. There might be mechanisms which compensate for the imbalance in injected and downward flow rate, perhaps changing the thickness of the solidified shell, thereby decreasing the length or width of the air gap, and consequently changing downward gas flow rate. It would be very surprising to find that the solidification process could stabilize itself in this fashion, but it should not be ruled out. The most probable casting situation would however seem to be a nonzero mean downward discharge combined with an excess of injected gas leading to periodic gas discharge up through the mould. A better understanding of slip gas flow will be sought in the current work.

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Chapter 2 Casting experiments

Casting table Holding furnace

Test mould

Figure 2.1: Casting setup.

A series of test castings were performed using pure aluminium and Al 6082, with both pure Argon and a mixture of 90% argon and 10% oxygen for injection in the mould. Casting velocities used were 90mm/min, 100mm/min, 120mm and 160mm/min. The ingot dia- meter was 200mm.

The casting set-up is displayed in figure 2.1. There were six pairs of moulds.

The test mould is indicated.

The placing of the thermocouples for temperature measurements are shown in figures 2.2 and 2.3. The tem-

perature was measured in four different regions; at several points close to the surface of the graphite ring in the mould, at the bottom of the hot-top, in the aluminium mould encapsulating the graphite (mould temperature) and at the melt surface in the mould (bath temperature). Thermocouples 1 and 3 in the graphite were not functioning during the tests.

The pressure in the gas pocket was measured using a Fischer Porter dif- ferential pressure transmitter. The meniscus was also videotaped during the experiments through an endoscope. Holes were made through the hot top for the pressure measurements and videotaping. The movement of the melt

21

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22 CHAPTER 2. CASTING EXPERIMENTS

Figure 2.2: Positioning of thermocouples in cross section of graphite ring and mould wall.

surface in the moulds was observed visually. Frequencies of oscillations were measured with the aid of a stopwatch. To facilitate visual observations a mould other than the test mould was observed.

Chemical analysis of pure Al and the Al 6082 alloy (weight %) is shown in the following table.

Al Fe Si Mg Mn other

Pure Al 99.68 .15 .13 .006 .03 .004 Al 6082 97.70 .18 .96 .62 .52 .02

2.1 Tests

A total of seven test castings were performed. Initially the aim was to cast four ingots with all four combinations of alloy and gas. Each ingot was to be cast in three 1- meter sections with casting velocities of 90mm/min, 120mm/min and 160mm/min. Due to problems experienced during the tests three castings were made for the case with pure Al, Ar10%O₂ and

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2.2. FREQUENCY ANALYSIS 23

Figure 2.3: Placing of thermocouples in hot-top cross section (1mm from bottom surface).

two castings were made with Al 6082, Ar10%O2. The following table gives an overview of castings. Cast ingots are numbered from 1 to 7.

Alloy 90mm/min 100mm/min 120mm/min 160mm/min Gas

Pure Al 1 - 2/3 2/3 Ar10%O2

- - - 4 4 Ar

Al 6082 5 6 6 6 Ar10%O2

- - 7 7 7 Ar

It was observed that for 160mm/min casting velocity the oscillatory behaviour in the test mould differed significantly from that of the other moulds.

So at this casting velocity the setup seemed to influence the casting more than at the lower casting velocities. Raw data for a section of ingot 6 are plotted in figure 2.4.

2.2 Frequency analysis

A frequency analysis of the temperature and pressure measurements were performed using the Fast Fourier Transform. Results for ingot 6 are presented in appendix A. From the frequency analysis the following higher characteristic frequencies [Hz] were found.

Pure Al 0.89 - 0.62 0.93 Ar10%O2

- - - 0.68 0.81 Ar

6082 - 0.45

0.89

0.49

0.98 0.90 Ar10%O2

- - - 0.55

(1.08) - Ar

The figures in italics are common modes of oscillation for temperature and

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400 402 404 406 408 410 412 414 416 418 420

100 200 300 400 500 600 700

Time [s]

temperature [deg C]

ht1 ht2 ht3 ht4

(a) Hot-top temperature.

400 402 404 406 408 410 412 414 416 418 420

50 55 60 65 70 75

Time [s]

temperature [deg C]

tc2 tc4 tc5 tc6

(b) Graphite ring temperature.

400 402 404 406 408 410 412 414 416 418 420

−0.3

−0.2

−0.1 0 0.1 0.2 0.3

Time [s]

Pressure [mbar]

(c) Gas pocket pressure variation.

Figure 2.4: Raw data, Al 6082, 90% Ar 10% O₂, 120mm/min

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2.2. FREQUENCY ANALYSIS 25

(a) (b) (c)

(d) (e) (f)

Figure 2.5: One period of oscillation (∼2s) for Al6082 with 90%Ar 10%O₂. pressure. Modes only appearing in the pressure signal are displayed in normal font.

The lower frequencies observed (of order 0.1Hz and lower) are not discussed here, since they represent a time scale that will not be used in the numerical simulations. These slow variations are possibly due to thermome- chanical coupling between the ingot contraction and secondary cooling. And variations in the temperature field will affect the properties of the molten aluminium at the meniscus, so they will influence meniscus behaviour on the time scale of the casting. For simplicity the variations will however be neglected in this thesis, where constant thermal boundary conditions are applied for the secondary cooling.

Characteristic period with meniscus collapse

A series of pictures for a period of meniscus oscillation for Al6082 with 90%Ar 10%O₂ at 120mm/min casting velocity is shown in figure 2.5. The

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(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j)

Figure 2.6: Meniscus collapse (∼.1s) for Al6082 with 90%Ar 10%O₂.

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2.3. DISCUSSION 27 meniscus collapse at the end of the period is shown in series 2.6. In the pictures the meniscus is viewed from above. The mould wall is seen below right while the meniscus surface is above left. Patches of lubricating oil can be seen on the mould wall and some fissures in the surface oxide layer may be discerned on the meniscus. These fissures disappear down along the mould wall as the meniscus collapses. There is approximately equal time spacing between the pictures in the individual series.

During a period (figure 2.5) the meniscus can be seen to move slowly downwards along the mould wall, 2.5(a) to 2.5(e), before it rapidly moves back up to its highest level, 2.5(f). At the end of this rapid upward movement the meniscus folds, or collapses. This collapse is seen in 2.6(f) to 2.6(i), where the resolution is poorer than in the other pictures due to the rapid folding process.

Surface oscillations

The frequencies of oscillation [Hz] of the visually observed melt surface in the mould are summarized in the following table. The oscillations were timed with a stopwatch.

Pure Al 3.00 - 0.66 0.81 Ar10%O2

- - - 0.59 1.00 Ar

Al 6082 - 0.43 0.50 0.71 Ar10%O2

- - - 0.43 1.11 Ar

The frequencies coincide quite well with the modes common to pressure and graphite temperature oscillations for casting velocities of 100mm/min and 120mm/min (again apart from the pure Ar cases, where the oscillatory signals are weak). But the modes only appearing in the pressure signal do not correspond very well to the manually measured frequencies.

2.3 Discussion

Common modes

It can be seen that the common modes exist mainly for medium casting velocity (120mm/min). With a casting velocity of 160mm/min the noise is greater than for the lower casting velocities and characteristic frequencies are more difficult to discern.

Significant oscillatory modes common to mould temperature, graphite temperature and gas pocket pressure only occur in Al 6082. They correspond

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Relative signal strength

0 0.5 1

1: Al, Ar10O2, 90 2: Al, Ar10O2, 120 2: Al, Ar10O2, 160 3: Al, Ar10O2, 120 3: Al, Ar10O2, 160 4: Al, Ar, 120 4: Al, Ar, 160 6: 6082, Ar10O2, 100 (*) 6: 6082, Ar10O2, 120 (*) 6: 6082, Ar10O2, 160 (*) 7: 6082, Ar, 120 7: 6082, Ar, 160

Ingot no. and section

Pressure Graphite temperature

Figure 2.7: Relative peak signal strength of oscillations in pressure and graphite temperature.

to the modes with high signal strengths for graphite temperature oscillations for ingot 6.

The common temperature oscillations observed for mould and graphite temperature are to be expected considering the frequency and the signal strength of these oscillations in the graphite. They occur however only for the ingots with alloy 6082, indicating more contact at the bottom of the mould, where the ingot is in thermal contact with the Aluminium part of the mould (see figure 2.2). The reason for the difference in contact is probably the difference in contraction experienced by 6082 and pure aluminium at this point.

Temperature oscillations

Figure 2.7 shows that in relation to the casting velocity the peak graphite temperature signal strengths are strongest for the 120mm/min castings, be-

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2.3. DISCUSSION 29 ing an order of magnitude greater than for the 100 and 160 mm/min sections of ingot 6 (Al 6082, Ar1%O2). Graphite temperature peak signal strength is generally low for castings with no oxygen, with the only significant peak for ingot 7 (Al 6082, Ar) at 120mm/min. These results imply that both oxygen and alloying elements enhance the periodicity and dampen the noise, with the oxygen possibly having a larger influence than the alloy elements. And the combined effect gives oscillations an order of magnitude stronger than that due to only oxygen or alloy elements.

Pressure oscillations

The peak signal strengths of the pressure oscillations (figure 2.7) have smaller variations (except for the 1 ingot, which froze in the mould). The pressure mode peaks for 160mm/min casting velocity are the largest for the pure aluminium ingots, while the peaks for 120mm/min are the largest for the Al 6082 ingots. Also, for the Al 6082 ingots there are dual pressure mode peaks for the 120mm/min sections. These dual peaks may imply higher harmonics.

The higher harmonic modes observed may be linked to a wave propagating on the meniscus. And the first mode could be coupled with the gravitational oscillations observed on the melt surface in the mould (see above). No observed higher harmonic modes at 160mm/min could be due to lowering of the contact point of the meniscus, giving reduced thermal contact with the wall. A smaller primary cooling area will also stabilize the process.

The peak signal strength of the graphite temperature oscillations is significantly stronger than the signals for mould temperature and pressure oscillations in the analysis (figure 2.7). This can also be observed in the raw data.

And the oscillations in pressure are a lot more erratic than the oscillations in the graphite temperature (figure 2.4).

Pressure spikes It is possible that the effect of the dual pressure peak is an artificial effect caused by regular interruption of the natural pressure signal following a meniscus collapse by the next collapse. An indication of this is the regularly appearing spike at the local temperature minima. This is assumed to be the point of the meniscus collapse (see figure 2.8). This being the case, a new characteristic pressure signal might be initiated, indicated by a spike¹, a sharp peak or through, at each point of collapse.

The direction of the pressure spike might be an indication of the gas pocket behaviour during folding, a strong upward spike indicating significant

1These spikes are seemingly not due to singular experimental error, since the width of a spike is several times the sampling interval.

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400 402 404 406 408 410 412 414 416 418 420

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

normalized

time [s]

pressure tc2

Figure 2.8: Comparison of normalized pressure in gas pocket and temperature for second thermocouple.

upward bubbling and a strong downward spike indicating folding without upward bubbling. To understand these effects the behaviour of the metal head must be considered in the collapsing process. As the meniscus collapses the metal head will decrease due to increased velocity of metal flow into the mould, and the extra metal momentum will displace gas in the pocket.

Now if the gas can escape quickly upwards the volume in the gas pocket can decrease without pressure buildup. The pressure in the gas pocket may therefore drop proportionally with the drop in metallostatic head. After the collapse, the reduced metal level will quickly fill. Thereby a negative spike in pressure is created. Gravity waves may be excited by the variations in metal level, resulting in further pressure variations, but now of a more sinusoidal nature.

In the opposite case, where there is no upward gas discharge, the gas can not escape quickly as the volume of the gas pocket is reduced by the momentum of the collapse. In this case the pressure will quickly build up as the gas volume is decreased by the metal momentum and then fall again as the gas expands by the force of its own pressure. So a positive pressure spike is created.

If the interpretation above is correct the type of gas discharge can be directly observed from a comparison of the pressure and temperature signals, giving an effective experimental method for observing meniscus behaviour.

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2.3. DISCUSSION 31

22.533.544.555.5640

45

50

55

60

65

70

75

80

85

90 Relative temp, mould wall

Thermocouple

Al , Ar10%O2 120mm/min 160mm/min 22.533.544.555.564045505560657075808590 Relative temp, mould wall

Thermocouple

Al , Ar 120mm/min 160mm/min 22.533.544.555.564045505560657075808590 Relative temp, mould wall

Thermocouple

Al 6082, Ar10%O2 100mm/min 120mm/min 160mm/min 22.533.544.555.564045505560657075808590 Relative temp, mould wall

Thermocouple

Al 6082, Ar 120mm/min 160mm/min Figure2.9:Meanmouldwalltemperatures.

Graphite temperature profile

The test data imply good thermal contact between graphite and ingot surface up to thermocouple 4 (see figures 2.9) for 120mm/min with pure aluminium.

For 160mm/min the contact is lower.

When Al 6082 is used, there appears to be contact up above thermocouple 2 for 120mm/min. With 160mm/min casting velocity the temperature gradient implies contact below the lowest thermocouple but the measured temperatures are exceptionally high when oxygen is used.

The indication of lowering of the meniscus at the mould wall coincides

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32 CHAPTER 2. CASTING EXPERIMENTS with observations in the mould during casting. In general, the lower meniscus contact point is lowered when casting velocity is increased. And both added oxygen in the slip gas and added alloy elements increase thermal contact with the mould wall, the former to a greater extent. This might also be explained by increased oscillations with larger amplitudes causing more thermal contact with the mould wall.

Elastic eigenmodes

If the mushy zone reaches above the lower point of the meniscus the movement will become more elastic than Newtonian. Consequently eigenfrequen- cies coupled to the elasticity might appear. The oxide layer on the surface of the melt could also influence eigenmodes. The combined effect is a lot stronger, and obviously not linear (see figure 2.7). This effect is not yet understood.

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Chapter 3 Analysis of wave phenomena

3.1 Introduction

In the experimental measurements of the temperature oscillations close to the meniscus in direct chill casting of aluminium ingot (see [17]), the characteristic frequencies are found to be around 0.5 and 1.0 Hz. These results are for castings of aluminium ingot with a radius of 200mm and casting velocity of 90 to 160 mm/s.

In this chapter different types of wave phenomena are analyzed to as- certain which wave phenomena could induce the observed characteristic frequencies. For different types of wave phenomena are analyzed. These are:

capillary waves on a meniscus of spherical section

coupledcapillary gravity waves on a meniscus of spherical section gravitational oscillations in casting column

coupledgravity pressure oscillations

The assumption of a steady state meniscus of cylindrical cross section is quite rough, since the curvature of a steady state meniscus will increase monotonously with the metal depth. However, for a small enough meniscus, this assumption will become valid. Ideally a solution for gravity/capillary waves should be sought for the type of meniscus, or free surface, obtained in the simulations (as in for example figures9.9(b)). But here the analysis will be restricted simple geometries and to the phenomena listed above. The stability of the solutions will also be considered.

33

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34 CHAPTER 3. ANALYSIS OF WAVE PHENOMENA

Figure 3.1: Coordinate system and capillary wave on the meniscus.

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3.2. CAPILLARY WAVES ON MENISCUS 35

3.2 Capillary waves on meniscus

Laplace equation

With the assumption of incompressibility and potential or irrotational flow, the velocity potential ψ in the meniscus region must fulfill the 2D Laplace equation:

∂²ψ

∂r² + 1 r

∂ψ

∂r + 1 r²

∂²ψ

∂θ² = 0. (3.1)

See figure 3.1 for description of coordinate system. The velocity components are

v_r = ∂ψ

∂r andv_θ = ∂ψ

∂θ. (3.2)

Boundary conditions (wave equation)

The boundary condition on the meniscus can be found by a variational analysis (as is done for the derivation of the spherical capillary wave equation in Landau and Lifshitz [40]). The change in meniscus surface area A will correspond to

A= Z Z

s r²+

∂r

∂θ 2

dθdz. (3.3)

Here a cylindrical coordinate system is applied with axis at z = 0 (normal to the plane shown in figure 3.1), then for variations of small amplitudes ζ (compared to wavelength), we have r =R+ζ on the meniscus, where R is the constant average radius, i.e. ζ R . Using a truncated binomial series, and neglecting terms of order ζ² and higher, gives the approximate result

A≈ Z Z

r+ 1 2R

∂ζ

∂θ 2!

dθdz. (3.4)

The change in surface area du to wave motion can subsequently be expressed by (see [23]):

Z Z

∂I_ζ

∂ζ − d dθ

∂I_ζ

∂ζ˙

δζ dθ dz, (3.5)

where I_ζ and ˙ζ are defined by I_ζ =r+ _2R¹ ^∂ζ_∂θ²

and ˙ζ = ^∂ζ_∂θ. As a result, δA=

Z Z 1− 1

R

∂²ζ

∂θ²

δζ dθ dz. (3.6)

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36 CHAPTER 3. ANALYSIS OF WAVE PHENOMENA In [40] it is shown that

δA= Z Z

δζ 1

R₁ + 1 R₂

r dθ dz, (3.7)

with Ri as the principle radii of curvature. For an ideal fluid, neglecting the influence of gravity and defining σ as the uniform surface tension coefficient, pas the pressure in the fluid and p₀ as the pressure outside the fluid (above the meniscus, see figure 3.1), then by [40]:

p−p₀ =σ1

R (3.8)

For capillary waves with incompressible fluids and adiabatic conditions we have, again by [40],

p=−ρ∂ψ/∂t, (3.9)

whereρis the density of the fluid. Equating the integrands in expressions 3.6 and 3.7, applying r = R+ζ, and including relations 3.8 and 3.9 we get to the first order inζ

−

ρ∂ψ

∂t +p₀

=σ 1

R + ζ R² − 1

R²

∂²ζ

∂θ²

. (3.10)

Taking the derivative with respect to time, linearizing and using the relation

∂ζ

∂t =v_r = ^∂ψ_∂r, the boundary condition on r=R becomes:

ρ∂²ψ

∂t² + σ R²

∂ψ

∂r − σ R²

∂

∂r

∂²ψ

∂θ² = 0, (3.11)

r =R.

Eigenfunction solution

The Laplace equation for the velocity potential can be solved using the method of eigenfunction expansions, or separation of variables. Since this corresponds to a regular Sturm-Liouville problem, the eigenfunctions are or- thogonal and linearly independent. With the separation

ψ =T(t)Q(θ)P(r), (3.12)

the resulting equations are

∂²Q

∂θ² =−ν²Q, (3.13)

r²∂²P

∂r² +r∂P

∂r =ν²P. (3.14)

Meniscus Dynamics in Aluminium Extrusion Ingot Casting

Preface

Summary

Contents

Chapter 1

Al ingot casting

1.0.1 A brief history of aluminium ingot casting

1.1 Process description

1.2 Solidification

1.2.1 Hot top

1.2.2 Mould geometry

1.2.3 Lubrication and gas injection

1.2.4 Cooling

1.2.5 Mushy zone

1.2.6 Heat transfer

1.2.7 Contraction

1.2.8 Segregation

1.2.9 Grain structure

1.2.10 Solidified surface

1.3 Meniscus dynamics

1.3.1 Surface tension and Wetting

1.3.2 Oxidation

1.3.3 Meniscus oscillations

1.3.4 Slip gas flow

Chapter 2

Casting experiments

2.1 Tests

2.2 Frequency analysis

2.3 Discussion

Chapter 3

Analysis of wave phenomena

3.1 Introduction

3.2 Capillary waves on meniscus